How do I remove the overlap from merged meshes?
You could do it with the TinyCAD addon or with some extrudes.

If you want to start with your 3 parallelepipeds you could use the TinyCAD addon:


Download and istall the addon.
Join your parallelepipeds with a ctrlJ, and go in Edit mode.
Select all and press W > TinyCAD > XALL.
Keep everything selected and press W > Remove Doubles.
Delete the inner vertices so that you won't have any inner edges in the final object.
Fill all the faces.




If you want to do it with some extrudes, you could:


Start with a plane, create an edge loop on its middle and tilt it with GG.
Bevel the middle edge loop with ctrlB and create 2 new edge loops.
Extrude the plane.
Select a face and press ctrlaltspacebar to create a new custom Transformation Orientation (named "Face.001" by default).
Keep this new orientation selected.
Select one of the faces you need to extrude, press E and Enter right away.
Move this new face along the Face.001 Y axis.
Same thing for the other face.